differenciate descriptive statistic from inferencial statistics with accurate example

Descriptive Statistics and Inferential Statistics are two broad categories in the field of statistics.

1. Descriptive Statistics: This type of statistics deals with the presentation and collection of data. It is used to describe the basic features of the data in a study. It provides simple summaries about the sample and the measures. For example, if we have data about the marks of 100 students in a class, descriptive statistics will allow us to present that data in a meaningful way, showing patterns, trends or relationships. This could be through numerical calculations such as averages and variances, or through graphs, charts or tables.

2. Inferential Statistics: This type of statistics takes data from a sample and makes inferences about the larger population from which the sample was drawn. It is the process of using data analysis to deduce properties of an underlying probability distribution. For example, if we have data about a sample of 100 students from a population of 1000 students, we can use inferential statistics to draw conclusions about the entire population of students (like estimating the average marks, predicting the proportion of students who will pass, etc.), based on the sample data.

In summary, descriptive statistics simply describe what is in the data, while inferential statistics help us make predictions or inferences about what the data can tell us about a larger group or population.